David Moyes is desperate to bolster his squad with an attacking player before Monday's 11pm deadline, with Trossard believed to be the latest name on their radar.
According to Football Insider, the Hammers have made contact with Brighton regarding the availability of the 27-year-old, but they are yet to have tabled a formal offer.
Trossard has just under 18 months remaining on his contract at the Amex Stadium, with talks yet to commence over an extension.
The Belgium international has been a key player under head coach Graham Potter since arriving from Genk in the summer of 2019, scoring 14 goals and providing nine assists in 87 Premier League appearances.
West Ham have also been strongly linked with Leeds United duo Kalvin Phillips and Raphinha, while the likes of Reims' Hugo Ekitike and Everton's Dominic Calvert-Lewin are also being closely monitored.